Related papers: On Unique Error Patterns in the Levenshtein's Sequ…

We introduce a fully constructive characterisation of holographic quantum error-correcting codes. That is, given a code and an erasure error we give a recipe to explicitly compute the terms in the RT formula. Using this formalism, we employ…

DNA has immense potential as an emerging data storage medium. The principle of DNA storage is the conversion and flow of digital information between binary code stream, quaternary base, and actual DNA fragments. This process will inevitably…

Motivated by DNA-based data storage, we investigate a system where digital information is stored in an unordered set of several vectors over a finite alphabet. Each vector begins with a unique index that represents its position in the whole…

Mechanistic interpretability is concerned with analyzing individual components in a (convolutional) neural network (CNN) and how they form larger circuits representing decision mechanisms. These investigations are challenging since CNNs…

Recurrent Neural Network (RNN) and its variations such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), have become standard building blocks for learning online data of sequential nature in many research areas, including…

This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…

Recent works have shown that modern machine learning techniques can provide an alternative approach to the long-standing joint source-channel coding (JSCC) problem. Very promising initial results, superior to popular digital schemes that…

Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…

Levenshtein introduced the problem of constructing $k$-deletion correcting codes in 1966, proved that the optimal redundancy of those codes is $O(k\log N)$, and proposed an optimal redundancy single-deletion correcting code (using the…

Speaker-independent speech separation has achieved remarkable performance in recent years with the development of deep neural network (DNN). Various network architectures, from traditional convolutional neural network (CNN) and recurrent…

Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error…

Nanopore sequencing, superior to other sequencing technologies for DNA storage in multiple aspects, has recently attracted considerable attention. Its high error rates, however, demand thorough research on practical and efficient coding…

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…

The quantum channel decomposition techniques, which contain the so-called probabilistic error cancellation and gate/wire cutting, are powerful approach for simulating a hard-to-implement (or an ideal) unitary operation by concurrently…

There exist many problem domains where the interpretability of neural network models is essential for deployment. Here we introduce a recurrent architecture composed of input-switched affine transformations - in other words an RNN without…

This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…

Recurrent neural networks (RNNs) are notoriously difficult to train. When the eigenvalues of the hidden to hidden weight matrix deviate from absolute value 1, optimization becomes difficult due to the well studied issue of vanishing and…

Feedforward Neural Network (FNN)-based language models estimate the probability of the next word based on the history of the last N words, whereas Recurrent Neural Networks (RNN) perform the same task based only on the last word and some…

Constrained sequence (CS) codes, including fixed-length CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy…

``Leakage'' errors are particularly serious errors which couple states within a code subspace to states outside of that subspace thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for…